On shortest paths in polyhedral spaces
SIAM Journal on Computing
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Unobstructed shortest paths in polyhedral environments
Unobstructed shortest paths in polyhedral environments
On-line construction of the convex hull of a simple polyline
Information Processing Letters
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Shortest paths help solve geometric optimization problems in planar regions
SIAM Journal on Computing
Visibility and intersectin problems in plane geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Computational Geometry in C
Direct methods with maximal lower bound for mixed-integer optimal control problems
Mathematical Programming: Series A and B
Block-structured quadratic programming for the direct multiple shooting method for optimal control
Optimization Methods & Software
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We use the idea of the direct multiple shooting method (presented by Bock in Proceedings of the 9th IFAC World Congress Budapest, Pergamon Press, 1984, for solving optimal control problems) to introduce an algorithm for solving some approximate shortest path problems in motion planning. The algorithm is based on a direct multiple shooting discretization that includes a collinear condition (a continuity condition type in the direct multiple shooting method), multiple shooting structure, and approximation conditions. In the case of monotone polygons, it is implemented by a C code, and a numerical example shows that our algorithm significantly reduces the running time and memory usage of the system.